List of practice Questions

From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $ {{90}^{o}} $ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $k$ times $ M{{R}^{2}} $ . Then the value of $k$ is

A liquid is filled upto a height of $20\, cm$ in a cylindrical vessel. The speed of liquid coming out of a small hole at the bottom of the vessel is $(g = 10 \; ms^{-2})$

A body is thrown up with a speed $u$, at an angle of projection $\theta$. If the speed of the projectile becomes $\frac{u}{\sqrt{2}}$ on reaching the maximum height, then the maximum vertical height attained by the projectile is

An engine of power $58.8\, kW$ pulls a train of mass $2 \times 10^{5}\, kg$ with a velocity of $36\, kmh ^{-1}$. The coefficient of friction is

A force F is applied on a square plate of side L. If percentage error in determination of L is 2% and that in F is 4%, permissible error in pressure is

If 10% of a radioactive material decays in 10 days the percentage of the material that decays in 20 days is

Ekta earns 3000 Rs. in 10 days. How much will she earn in 30 days?

\(∫\frac{dx}{e^x+e^{-x}}\) is equal to

A plane electromagnetic wave travelling along the $ X- $ direction has a wavelength of $ 3 \,mm $ . The variation in the electric field occurs in the $ Y- $ direction with an amplitude $ 66\,V{{m}^{-1}} $ . The equations for the electric and magnetic fields as a function of $ x $ and $t$ are respectively.

A ball dropped from a height of $2\,m$ rebounds to a height of $1.5\,m$ after hitting the ground. Then the percentage of energy lost is

Are the following statements true?
(a) 40 persons: 200 persons = ₹15: ₹75
(b) 7.5 litres : 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = ₹ 44: ₹20
(d) 32 m: 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours

Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?

An edge of a variable cube is increasing at the rate of \(3 cm/s\). How fast is the volume of the cube increasing when the edge is \(10 cm\) long?

A Cassegrain telescope uses two mirrors as shown in Fig. 9.26. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

Choose the wrong statement.

A man of mass $60 \,kg$ climbed down using an elevator. The elevator had an acceleration $4 \, ms^{-2}$. If the acceleration due to gravity is $10 \, ms^{-2}$, the main apparent weight on his way down is

Which one of the following pairs consists of only paramagnetic species?

A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane .Then

According to Kepler's law of planetary motion if $ T $ represents time period and $ r $ is orbital radius, then for two planets these are related as :

Ampere?s circuital law can be derived from

Which one of the following has the smallest bond angle ?

An electric dipole of dipole moment $\overrightarrow{p}$ is placed in a uniform external electric field $\overrightarrow{E}$. Then the

An odd electron molecule among the following is

Huygen's wave theory of light could not explain

Ice pieces are floating in a beaker $A$ containing water and also in a beaker $B$ containing miscible liquid of specific gravity $1.2$. When ice melts, the level of